In recent years, banks across the country have been offering checking accounts and even mortgages to the nation's fast-growing ranks of undocumented immigrants, most of whom are Hispanic, the paper said, adding these immigrants generally have not been able to get major credit cards.

The new Bank of America card is open to people who lack both a Social Security number and a credit history, as long as they have held a checking account with the bank for three months without an overdraft, the Journal said.

Bank of America tested the program last year at five branches in Los Angeles, and last week expanded it to 51 branches in Los Angeles County, home to the largest concentration of illegal immigrants in the U.S., the Journal said.